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The final ranking
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Which is the fifth-best team in one-day international cricket today?M J Manohar Rao and Srinivas BhogleIn November 2001 we proposed the Rao-Bhogle index (RBI) to rank international teams playing Test cricket. The response to this rating scheme was very positive and we were asked if we could propose a comparable scheme to rate the performances in one-day international (ODI) cricket. In this note we explain how we came up with the RBI for ODI matches (ODI RBI). The exercise was interesting, with some worries and surprises. But we think that we have come up with an index which performs just as well. ODI vs Test cricket There are some significant differences between Test and ODI cricket: (a) ODI's always have a result, except for the occasional tie. (b) Many ODI's are played as a part of a tournament, involving three or more teams. A tournament also has a final (and sometimes even semi-finals), which is considered to be more "important". (c) Instead of always playing either at 'home' or 'away', teams could now also be playing at neutral venues. Desirable criteria As in the Rao-Bhogle index for Test cricket, we will require ODI teams to:
Towards a "suitable" index As before, we will agree that every win is worth 1 point and every defeat is worth 0 points. The unlikely tie, when it occurs, would fetch each team half a point. We will also not award bonus points for tournament finals and semi-finals. We did briefly consider bonus points for these more "important" games, but eventually gave up the idea because we couldn't think of a sufficiently objective procedure to award these bonus points. ODI matches are played either as a part of a series between two opposing teams, or as a tournament featuring three or more teams. While it is easy to handle ODI series between two teams, tournaments are more tricky: we have to consider tournaments played at one of the teams' home venues (e.g. the recent triangular series between South Africa, India and Zimbabwe at South Africa) and tournaments at 'neutral' venues like Sharjah. In the first case we have some matches of the 'home-away' type (such as SA vs Ind in SA), while others are of the 'neutral' venue type (such as Ind vs Zim in SA). We therefore decided to classify a team's points into three categories: (a) points from 'home' matches (which include both home series and home tournaments), (b) points from 'away' matches (from away series and away tournaments) and (c) points from matches at neutral venues. We further agreed to consider the most recent series and tournament encounters between two countries at home, away and at neutral venues. As an illustration, let us consider India vs Sri Lanka. India last met Sri Lanka in a 'home' series in 1997-98. This series was drawn 1-1 with one match abandoned. India last played Sri Lanka in a 'home' tournament during the 1998-99 Pepsi Cup in which India defeated Sri Lanka 2-0. So, in the most recent 'home' matches with Sri Lanka, India have 1+2=3 points out of 2+2=4 (and Sri Lanka therefore have 1 point out of 4 in their 'away' matches against India). India last played SL in an 'away' series at SL in 1997-98 when they lost all their three matches, with a fourth match abandoned. India's most recent 'away' tournament in SL was the Coca-Cola Cup in 2001 where India won two matches and lost two. So India's 'away' record against SL has 0+2=2 points out of 3+4=7. (Sri Lanka therefore have 5 points out of 7 in their 'home' tally against India). Finally, India's last meeting against Sri Lanka at a neutral venue was at Sharjah in 2001 when SL won three matches out of three (so SL have 3 points out of 3 against at a neutral venue, while India have 0 points out of 3).
In this manner, it is possible to construct the full 'matrix' (see Table A below, updated as on January 11, 2002) of home, away and neutral venue points for all the nine ODI playing teams being considered (we haven't included Kenya and Bangladesh). Our sample includes 446 of the most recent ODI matches, or about 25% of all the ODI games played so far.
A 'simple' performance index Table A is revealing. For example, if we add up South Africa's home, away and neutral points against all opponents we find that they have obtained 81 points over their last 113 matches. This gives South Africa a 'simple' percentage performance index of 71.68 (= 100 * 81 / 113 ). Similarly, if we add up India's points against all opponents, we find that India have obtained 54 points over their last 114 'home', 'away' and 'neutral venue' matches, giving them a much lower 'simple' performance index of 47.37 (= 100 * 54 / 114). In Table B, below, we provide the current 'simple' performance indices for the nine ODI playing teams being considered.
Table B tells us which team is winning the most matches and corresponds to our Criterion 1. It also contains the first surprise: if we look at the top two positions, it is South Africa (71.68) which have the better performance index -- not Australia (66.51) as some of us might have guessed. We also note that Sri Lanka (59.38) are in the middle of a good winning streak. India (47.37) are comfortable at the fifth position, confirming the widely held view that they play ODI cricket better than Test cricket (where they lie seventh in the Rediff ratings). Opponent-specific 'weighted' performance index It is, however, not appropriate to merely use these simple performance indices to rank the ODI playing countries. This calculation does not take into account the quality of the opposition (recall Criterion 2). After all, defeating South Africa or Australia is much more difficult than beating West Indies or Zimbabwe. A victory against South Africa must therefore be accorded a much higher 'weight' as compared to a win against Zimbabwe. Most analysts recognise this fact, but cannot agree on the opponent-specific 'weight' to be accorded under the circumstances. As we did in our Test cricket rating scheme, we will use these simple performance indices as the 'weights'. Thus a win against South Africa today will have a 'weight' of 0.7168, a win against India a 'weight' of 0.4737, a win against West Indies a 'weight' of 0.3889 ... and so on. This seems a fair way of classifying wins, and implies that a win against Australia is worth four wins against Zimbabwe (0.6651/0.1667 = 4), or a win against South Africa is worth almost two wins against the West Indies (0.7168/0.3889 = 1.9)! In Table C, below, we present the 'weighted' percentage performance indices of the nine ODI playing countries (using the same calculation procedure that we used for the Test ratings).
Table C, which builds in the 'opposition factor' into the performance index, shows that the top six teams retain their rankings, although West Indies just inch ahead of New Zealand in the fight for the 7-8 positions. A glance at the 'difference' column of Table C shows that Pakistan, India, England and Sri Lanka lose around 4 points suggesting some difficulty in defeating stronger opponents and a relatively greater propensity to defeat the weaker sides. South Africa, who gain marginally, are seen to have rather good winning records against the better teams like Australia and, especially, Pakistan. Opponent- and location-specific 'weighted' performance index The 'opposition-weighted' performance indices of Table C certainly offer a better assessment than the 'simple' performance indices of Table B. But we would like to argue that even Table C does not tell the whole story. We still haven't arrived at our "best" index, which must take into account all our three criteria: high win percentage + wins against stronger opponents + wins at all possible venues (Criteria 1, 2 &3). Generally speaking, teams play much better at home (with Pakistan being the notable exception; they actually do better outside their country!). In addition to this 'home-away' dichotomy, we have an additional -- and significant -- 'neutral venue' factor in ODI's (with Pakistan, again, being practically invincible at a venue like Sharjah). Our analysis must therefore take into account location-specific factors by using appropriate 'location-specific' weights. To do this, we will decompose the simple performance index of Table B into 'home', 'away' and 'neutral venue' performance indices and then see how these indices can be used as 'weights'. Table D, below, shows this decomposition.
Table D contains important pointers. For example, South Africa's home performance ratio is an amazing 81.03; so opponents, on the average, must lose five matches to gain one win on South African soil. In our opponent and location-specific index, therefore, defeating South Africa in South Africa would fetch 0.8103 points, while defeating South Africa when they are 'away' (e.g. in India) would fetch the opponent relatively lower (0.6111) points. We also note, for example, that defeating England when they are playing an 'away' series (e.g. in India) is worth 0.3367 points. So defeating Australia in Australia (0.7449), or, indeed, Pakistan at a neutral venue like Sharjah (0.7059) is worth more than two wins against a touring England team. Home wins against Sri Lanka (0.7209), West Indies (0.5854) and even India (0.5536) are also seen to be lucrative. On the other hand, defeating New Zealand (0.2368), West Indies (0.2555) and Zimbabwe (0.1875), when they are on away tours, isn't very profitable! We are now almost ready to compute our 'double-weighted' (opponent- and location-specific) Rao-Bhogle index for ODI's. Before we get there, however, there is one complication to overcome. Our difficulty with ODI's arises from the fact that we now have three weights (for home, away and neutral venues) and our 'location factor' for ODI's is a combination of the 'home-away' and 'neutral venue' factors. (Recall that the RBI for Test matches had only two weights -- for home and away venues -- and our 'double-weighted' index neatly captured the 'home-away effect' -- which indeed was the only 'location effect'). We struggled a little to solve this problem in view of the 'triple-weighted' nature of the index. Finally, we have adopted a methodology that is reliable and robust and yields an index that is easy to update. We initially assume that there are two kinds of ODI's: of the 'home-away' type and the 'neutral venue' type. For each type, and for each team, we compute the weighted index based on our established formula. Finally, we average these two indices in the proportion of the number of matches played. Table E, below, summarizes all these calculations.
Table E, which combines our Criteria 1,2 & 3, reveals a truly dramatic turnaround. In the 'last lap' Pakistan overtake Sri Lanka in a fiery burst to take the third position! We must confess that even we were surprised by this result. Pakistan gained due to two factors: first, because of their amazing ability to win 'away' matches (one suspects that 'home' conditions don't help Pakistan's versatile bowling attack enough; so only their 'weaker' batsmen must win it for them at home) and, second, due to the Sharjah factor (where, after one incredible last ball sixer by Miandad, Pakistan just don't know how to lose). Sri Lanka's index is higher than Pakistan's (51.22 - 49.71 = 1.51) if we only look at their 78 (and Pakistan's 80) 'home-away' matches. Sri Lanka eventually lost because they could not match Pakistan's incredible success at neutral venues (mostly at Sharjah). Sri Lanka's opponent-specific neutral venue index of 57.64 (from 18 matches) was much less than Pakistan's matching index of 66.04 (from 17 matches). So, in the final count, it was the Sharjah factor which took Pakistan to its third position. The mini-battle between West Indies and New Zealand for the 7-8 places is also interesting. Here, NZ are seen to have a much higher opponent-specific neutral venue index (49.22 from 12 matches) than West Indies (17.89 from 13 matches). But WI's big lead (39.14 - 33.34 = 5.80) in the home-away index (over 85 and odd matches) helps them retain the seventh place. Since both WI and NZ play badly in 'away' matches, it was finally WI's better home performance that took them past NZ. Other pointers from Table E show South Africa's greater relative dependence on home wins (although the champion team still has a wonderful frequency of 'away' wins). The 'home' factor also appears more important to Sri Lanka and India. Australia and New Zealand too would rather play at home. Zimbabwe, sadly, appear to be incapable of winning anywhere -- at home, away or at neutral venues. The final rankings Table F, for the record, lists the final ODI RBI rankings as on January 11, 2002.
Table F suggests some very interesting duels: SA vs Aus for the top two positions (Australia, however, have some work to do to overtake South Africa); SL vs Pak (SL are doing wonderfully well, especially as a team, but Pakistan have much more talent and the ability to surge ahead if challenged); Ind vs Eng (which will be close, with England having the opportunity to gain more points if they defeat India in India) and WI vs NZ (which remains too close to call). As always, the ODI RBI for all the teams will rise or fall after every series or tournament; but they would always provide good pointers of every team's current form. We would welcome suggestions from our readers -- in particular, we still await an objective scheme which will correctly reward winners of tournaments. We are confident that we will find this scheme well before the 2003 World Cup tournament. Table F, incidentally, also answers the question posed in this paper's title: India is currently the fifth best team in one-day international cricket.
Acknowledgements To obtain all the Test match results we used the data available on Cricinfo. We are grateful to someone dear to both of us who did all the data collection, tabulation and calculations. We thank Rediff and Prem Panicker for starting the Rediff ratings micro-site, and our numerous correspondents for encouraging us to undertake this rather involved exercise.
M J Manohar Rao is professor and director, Department of Economics,
University of Mumbai, Mumbai; Srinivas Bhogle is scientist and head,
Information Management Division, National Aerospace Laboratories, Bangalore.
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